The gray code is a binary numeral system where two successive values differ in only one bit.

Given a non-negative integer n representing the total number of bits in the code, print the sequence of gray code. A gray code sequence must begin with 0.

For example, given n = 2, return [0,1,3,2]. Its gray code sequence is:

00 - 0
01 - 1
11 - 3
10 - 2

Note:
For a given n, a gray code sequence is not uniquely defined.

For example, [0,2,3,1] is also a valid gray code sequence according to the above definition.

For now, the judge is able to judge based on one instance of gray code sequence. Sorry about that.

一刷
题解：
利用backtracking, 从0到n，先计算用0开头的数,再计算用1开头的数, n++, 然后再在原先的基础上，开头添上0或1

Time Complexity - O(2n)

public class Solution {
    public List<Integer> grayCode(int n) {
        List<Integer> res = new ArrayList<Integer>();
        if(n<0) return res;
        if(n == 0){
            res.add(0);
            return res;
        }
        
        List<Integer> last = grayCode(n-1);
        res.addAll(last);//begin with 0
        int prefix = (1<<n-1);// begin with 1
        
        for(int i=last.size() -1; i>=0; i--){
            res.add(last.get(i) + prefix);
        }
        
        return res;
    }
}

二刷
1 <= i < 2^n
G(i) = i ^ i/2;

public class Solution {
    public List<Integer> grayCode(int n) {
        List<Integer> res = new ArrayList<>();
        for(int i=0; i<1<<n; i++){
            res.add(i ^ (i>>1));
        }
        return res;
    }
}